Getting Wavelet Basis functions

In summary, the conversation is about finding a Basis Matrix in Matlab for a 1D signal using wavelet packages. The person asking the question is not concerned about the type of wavelet and is not looking to find the wave coefficients using wavedec. They are looking for a Basis Matrix to compress a generic signal. Another person suggests looking into proper orthogonal decomposition and provides resources for guidance. The original person asks for clarification on whether the suggestion is for wavelets specifically and asks for specific search terms or recommended papers.
  • #1
sachin_ruk
2
0
Hi all,

Say that I have a 1D signal such that f=Bw where f is the signal B is the basis functions and w is the wave co-efficients. The question that I have is how do I find the B matrix in Matlab.

I am looking through WaveLab and Rice Wavelet packages but simply cannot find an answer. As for the type of wavelet, for the moment I'm not too worried. Note that I am not concerned about trying to find w by using wavedec or similar functions in Matlab. Simply want some sort of a Basis Matrix that will allow me to compress a generic signal.

Thanks,
Sachin
 
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  • #2
Look into proper orthogonal decomposition. There are some good papers/resources out there that can guide you.

Hopefully I didn't misinterpret your question.
 
  • #3
Hey thanks for the reply. I don't mean to be a bother, but were you talking about wavelets in particular or general orthogonal decompositions. If you were could you tell me what exactly to google, or maybe a paper that you would recommend?

Thanks,
Sachin
 

1. What are wavelet basis functions?

Wavelet basis functions are mathematical functions that are used to analyze signals and data in a time-frequency domain. They are a set of building blocks that can be combined to form a signal, and they are characterized by their ability to capture both local and global features of a signal.

2. How are wavelet basis functions obtained?

Wavelet basis functions are obtained through a process called wavelet decomposition. This involves breaking down a signal into its constituent parts at different scales, using a mathematical operation called convolution. The result is a set of wavelet basis functions that can be used to represent the original signal.

3. What are the advantages of using wavelet basis functions?

Wavelet basis functions have several advantages over other signal analysis methods. They can capture both local and global features of a signal, they are efficient in terms of computation, and they can handle non-stationary signals (signals that change over time). Additionally, wavelet basis functions have applications in a variety of fields, including signal processing, image compression, and data analysis.

4. How do you choose the right wavelet basis functions?

Choosing the right wavelet basis functions depends on the specific application and the characteristics of the signal being analyzed. Generally, the wavelet basis functions should have a good balance between time and frequency localization, and they should be able to capture the relevant features of the signal. It is also important to consider the computational efficiency and the interpretability of the chosen wavelet basis functions.

5. Are there any limitations to using wavelet basis functions?

While wavelet basis functions have many advantages, they do have some limitations. They may not be suitable for all types of signals, and the choice of wavelet basis functions may affect the results of the analysis. Additionally, the interpretation of wavelet analysis results can be challenging, especially for complex signals. It is important to carefully evaluate the suitability and limitations of wavelet basis functions for a specific application before using them.

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